Bump mapping is a kind of texture. The difference between bump mapping and regular texture mapping is that the reflections and lights on a bump mapped 3D model is different from a regular texture.

Two oranges made in 3D Studio Max: Both of them has a polycount on 1000, and is geometrically identical. one of the has bump mapping, one of them has regular texture. The one without bump mapping would look fake, and smooth. The one with bump mapping would have realistic reflections.